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From Estimation to Sampling for Bayesian Linear Regression with Spike-and-Slab Prior
We consider Bayesian linear regression with sparsity-indu cing prior and design efficient sampling algorithms leveraging posterior contraction properties. A quasi-likelihood with Gaussian spike-and-slab (that is favorable both statistically and computation ally) is investigated and two algorithms based on Gibbs sampling and Stochastic Localization are ana lyzed, both under the same (quite natural) statistical assumptions that also enable valid in ference on the sparse planted signal. The benefit of the Stochastic Localization sampler is particula rly prominent for data matrix that is not well-designed.